7.4 Regular polygons

1. 7.4 Regular polygons Objective: After studying this section, you will be able to recognize regular polygons and use a formula to find the measure of an exterior angle of an equiangular polygon.

2. A regular polygon is a polygon that is both equilateral and equiangular Regular polygons:a few examples Equilateral Triangle Regular Pentagon Square Regular Hexagon Notice anything in common between these polygons?

3. 1 In the last lesson you learned that the sum of the exterior angles is 360 for any polygon. In a regular polygon all the angles inside are equal so the exterior angles should be equal as well. If we take 360 and divide by 5 (there are 5 angles) we will get the measure of angle 1.

4. Theorem The measure E of each exterior angle of an equiangular polygon of n sides is given by the formula

5. Example 1 How many degrees are there in each exterior angle of an equiangular heptagon?

6. Example 2 If each exterior angle of a polygon is 18 degrees, how many sides does the polygon have? Example 3 If each angle of a polygon is 108 degrees, how many sides does the polygon have?

7. Example 4 Find the measure of each angle of a regular octagon Example 5 Find the measure of each exterior angle of an equilateral quadrilateral

8. Summary Explain why the statement “If a polygon is equiangular, then it is a regular polygon” is false. Homework Worksheet